Is the teacher's request for her students to swear on the Quran not to cheat considered a form of negligence, and is the teacher sinful for doing so?

Swearing by the Mus'haf (copy of the Quran): if what is intended by it is the speech of Allah, then it is a legitimate oath. However, if what is intended by it is the paper and the ink, then it is swearing by other than Allah, and this is a form of shirk (polytheism). It is preferable not to swear by the Mus'haf. Cheating is forbidden in all its forms, based on the saying of the Prophet, peace and blessings be upon him: "Whoever cheats is not of me." A female teacher asking female students to swear on the Mus'haf that they did not cheat is impermissible, because some of them may swear while they are lying, out of fear. The teacher's duty is to teach them truthfulness and trustworthiness, and to manage the exam properly.